"Explain how to solve the absolute value inequality | 3x + 6 | > 9 and give a rough sketch of the graph of the resulting solution."

I need help on how to solve this one. Thanks.

|3x + 9| > 9

Recall: |a| = ±a

So, (3x + 9)>9 or -(3x + 9)>9

Take (3x + 9) > 9.

Subtract 9 from each side.

3x > 0

Divide each side by 3.

x > 0

And - (3x + 9) > 9

Multiply each side by negative one and flip the symbol.

3x + 9 < -9

Subtract 9 from each side.

3x < -18

Divide each side by 3.

x < -6.

Therefore x > 0 or x < -6

Graph on the number line.

The given absolute inequality is |3x + 6| > 9.

The absolute inequality is |3x  + 6| > 9

|x | > a Then > a or x < -a

The absolute value of inequality |3 + 6| > 9 is equivalent to 3x  + 6 > 9 or 3x  + 6 < - 9

Solve the inequality 1: 3x  + 6 > 9

Subtract 6 from each side.

3x  + 6 - 6 > 9 - 6

3x  > 3

Divide each side by 3.

3x/3 > 3/3

Cancell common terms.

x  > 1

Slove the inequality 2: 3x  + 6 < -9

Subtract 6 from each side.

3x  + 6 - 6 < - 9 - 6

3x  < -15

Divide each side by 3.

3x/3 < -15/3

Cancell common terms.

x < -5

Solution x  > 1 or < -5.

The solution set is {x |x < - 5 or x > 1}

Graph of the solution on a number line.

Observe the graph , the open circle means that -5 and 1 does not solutions of the inequality.